The present invention relates generally to ferroresonant transformers, and more particularly to a method of designing a high power factor ferroresonant constant current source.
The industry""s choice of root-mean-square (rms) to measure AC voltage and current introduced the power factor concept. Power factor accounts for the discrepancy between kilovolt-ampere (kva) and kilowatt (kw), where kva is the multiplicative product of the rms current and voltage, and kw is the real power.                               I          RMS                =                                            1              T                        ⁢                                          ∫                0                T                            ⁢                                                                    i                    2                                    ⁡                                      (                    t                    )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                                                        (1)                                          V          RMS                =                                            1              T                        ⁢                                          ∫                0                T                            ⁢                                                                    v                    2                                    ⁡                                      (                    t                    )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                                                        (2)                                          P          Watts                =                              1            T                    ⁢                                    ∫              0              T                        ⁢                                                            i                  ⁡                                      (                    t                    )                                                  ·                                  v                  ⁡                                      (                    t                    )                                                              ⁢                              xe2x80x83                            ⁢                              ⅆ                t                                                                        (3)                                PF        =                              P            Watts                                              I              RMS                        ⁢                          V              RMS                                                          (4)            
where i(t) and v(t) are the instantaneous current and voltage, respectively, and T is the period. The power factor can be from 0, for pure inductive or capacitive loads, to 1.0 for resistive loadsxe2x80x94the higher the better. As can be seen from the above expressions, IRMSxc2x7VRMS=Pwatts only if the load is resistive. For non-linear loads, or inductive/capacitive loads, the real power Pwatts is less than IRMSxc2x7VRMS. It is important that an electrical load maintains a high power factor so as to reduce the current going to the load as well as the cost of cable and I2R losses.
Power factor has mostly been associated with inductive loads in which AC capacitors are incorporated to cancel the inductive current and correct any lagging power factor. The power factor in this case can be represented in terms of the cosine of the phase angle xcex1 between the voltage and the current: PF=cos(xcex1). The above power factor is also known as displacement power factor. There is another form of power factor that is associated with non-linear loads such as, for example, rectified capacitive loads, and is referred to as distortion power factor.
Ferroresonant transformers typically have an input power factor of 0.98 to 1.0, and are used to buffer both displacement and distortion power factor loads. A controlled ferroresonant constant current source varies the output current by controlling the conduction angle of an inductive reactance XL that is magnetically coupled to the resonant capacitor. The inductive discontinuous current introduces both displacement and distortion power factor. The distortion power factor can be reduced to virtually zero by increasing the capacitor leakage reactance XS. As a result, displacement power factor is the only form of power factor present in a ferroresonant transformer, which is contributed by the control inductive reactance XL.
A constant voltage ferroresonant transformer has a high input power factor since the inductive current contributed by the control inductive reactance XL is kept to a minimum. A controlled ferroresonant constant current source, on the other hand, requires the voltage to change over a wider range in order to maintain a constant load current. The effect of this inductive current, contributed by XL, reflected on the primary may reduce the input power factor to less than 0.2 during minimum output current sensing.
As shown in FIG. 1 and as explained more fully in my U.S. patent application Ser. No. 09/904,997, now U.S. Pat. No. 6,426,610, a simplified equivalent circuit 10 of a controlled ferroresonant constant current source shows the control inductive reactance XL external to the core of the ferroresonant transformer. This equivalent circuit is useful in deriving the expression for power factor as set forth below in equation 5. As shown in FIG. 2 and as also explained more fully in my U.S. patent application Ser. No. 09/904,997, now U.S. Pat. No. 6,426,610, another equivalent circuit 100 of a controlled ferroresonant constant current source shows the control inductive reactance XL integrated into the core of the ferroresonant transformer. This equivalent circuit is useful for deriving the expressions for the resonant capacitor gain A to be explained hereinbelow with respect to equations 6 through 14. The equivalent circuits of FIGS. 1 and 2 will briefly be explained prior to using them for deriving equations.
With reference to FIG. 1, the circuit 10 may be made to function as a constant current source by incorporating an output inductor, such as an output coil 12 and shunt 14 into the core of the ferroresonant transformer. In this instance, a control inductor 16 is employed externally of the transformer core.
As mentioned in my U.S. patent application Ser. No. 09/904,997, now U.S. Pat. No. 6,426,610, several factors were considered in developing an improved controlled ferroresonant constant current source. A linear inductor includes a steel core, a coil and an air gap. The inductance is determined by the core cross-sectional area, the number of turns, and the length of the air gap. As the power rating of a controlled ferroresonant current source increases, the resonant capacitance, capacitive current, and control inductive current increase, which requires the control inductor to have a lower value. To reduce the inductance of an inductor, the turns need to be reduced or the air gap increased. The cross-sectional area needs to be adjusted to maintain an acceptable maximum flux density. A large air gap poses serious thermal problems because of fringing flux, which cuts through the core laminations and the magnet wire at a high loss angle, producing eddy currents that overheat the inductor and reduce efficiency. Increasing the size of the magnet wire will further increase the magnitude of eddy currents and reduce efficiency.
Integrating the control inductor into the core of the ferroresonant transformer using magnetic shunts significantly reduces the gap loss heating effect. The air gap of the shunts is more effective in determining inductance and can be easily distributed into multiple air gaps of shorter lengths. If the control inductor is integrated with the transformer core, and the output inductor is external to the transformer core, then the inductor is subjected to the load voltage which may be extremely high in magnitude (i.e., 1000-5000V). A high voltage inductor requires a large number of turns with high electrical insulation between turns and layers. A large number of turns will also increase the resistive losses and reduce the efficiency.
It has been discovered that the controlled ferroresonant constant current source may be improved by integrating both the output inductor and the control inductor onto the core of the ferroresonant transformer while using standard EI laminations. In order for the controlled ferroresonant constant current source to operate, the control inductor must interface with the capacitor sub-circuit such that the currents are in phase.
With reference to the circuit 100 of FIG. 2 and as explained more fully in my U.S. patent application Ser. No. 09/904,997, now U.S. Pat. No. 6,426,610, it has been determined that drawbacks in integrating the output inductor and the control inductor are solved by creating two separate resonant sub-circuitsxe2x80x94one to interface with the load inductor including the output coil 102 and the shunt 104 to provide maximum gain, and another to interface with the control inductor, including the control coil 106 and the shunt 108 to control the resonant gain.
The benefits of incorporating both the control inductor and the output inductor onto the transformer core are 1) complete isolation between all circuits; 2) simplified wiring between the transformer core and external components; 3) low inductance, high current chokes no longer a limiting factor to increasing the power rating of the current source since shunts have a wider inductance range; and 4) permits the use of standard laminations which simplifies the assembly process.
Returning now to our discussion on power factor, since the distortion power factor can be greatly reduced by the proper choice of XS, the input power factor is predominantly the result of displacement power factor, PF=cos(xcex1), which may be derived from the circuit 10 of FIG. 1 and expressed in equation (5) as:   PF  =      1                                        1            +                          (                                                                                                                                                                                                      X                              S                                                        ⁡                                                          (                                                                                                                                    X                                    C                                                                    ⁢                                                                      X                                    L                                                                                                  -                                                                                                      X                                    L                                                                    ⁢                                                                      X                                    O                                                                                                  +                                                                                                      X                                    C                                                                    ⁢                                                                      X                                    O                                                                                                                              )                                                                                2                                                +                                                                                                                                                                                                      X                            L                                                    ⁢                                                      X                            C                                                    ⁢                                                                                    X                              O                                                        ⁡                                                          (                                                                                                                                    X                                    C                                                                    ⁢                                                                      X                                    L                                                                                                  -                                                                                                      X                                    L                                                                    ⁢                                                                      X                                    O                                                                                                  +                                                                                                      X                                    C                                                                    ⁢                                                                      X                                    O                                                                                                                              )                                                                                                      +                                                                                                                                                                                                      R                            2                                                    ⁡                                                      (                                                                                          X                                C                                                            -                                                              X                                L                                                                                      )                                                                          ⁢                                                  (                                                                                                                    X                                C                                                            ⁢                                                              X                                L                                                                                      -                                                                                          X                                S                                                            ⁢                                                              X                                L                                                                                      +                                                                                          X                                S                                                            ⁢                                                              X                                C                                                                                                              )                                                                                                                                                                                R                      S                                        ⁡                                          [                                                                                                    (                                                                                                                            X                                  C                                                                ⁢                                                                  X                                  L                                                                                            -                                                                                                X                                  L                                                                ⁢                                                                  X                                  O                                                                                            +                                                                                                X                                  C                                                                ⁢                                                                  X                                  O                                                                                                                      )                                                    2                                                +                                                                                                            R                              2                                                        ⁡                                                          (                                                                                                X                                  C                                                                -                                                                  X                                  L                                                                                            )                                                                                2                                                                    ]                                                        +                                                            X                      C                      2                                        ⁢                                          X                      L                      2                                        ⁢                    R                                                                                      )            2      
Even though XL is switched in and out of the circuit in a piecewise continuous fashion (see waveform of IL shown in FIG. 6), it is assumed to be continuously variable because of the filtering effect of XS, XO and XC.
FIGS. 7, 8, 9, 10 and 11 are plots of power factor versus changes in XC, XS, XL, XO and R. More specifically, FIG. 7 is a graph of curve 500 illustrating power factor over a limited range of values of the control inductive reactance XL. FIG. 8 is a graph of curve 600 illustrating the power factor over an extended range of values of the control inductive reactance XL. FIG. 9 is a three-dimensional graph of contour 700 illustrating power factor as a function of XS and XL. FIG. 10 is a three-dimensional graph of contour 800 illustrating power factor as a function of XO and XL. FIG. 11 is a three-dimensional graph of contour 900 illustrating power factor as a function of XC and XL.
These plots show that there exists an optimum set of values for XS, XC and XO that will result in the highest power factor. These values, normalized to R=1, are 0.7, 0.55 and 0.7, respectively. RS accounts for the resistance of all the windings and is assumed to be 0.01. In order to improve the power factor, XL must remain higher than 0.8, as shown in FIG. 7. Some applications require the minimum output current to be so low that XL would assume such a low value that the resulting input power factor would be less than 0.2 lagging. A commonly implemented solution for this lagging power factor is to introduce a power factor correction circuit on the primary, which comprises a capacitor or a combination of a capacitor and an inductor. While this may improve the power factor, it could cause the system to oscillate, particularly during a step load change or a step input voltage change, as well as distortion of the input current, and a reduction in the efficiency.
It is a general object of the present invention to overcome the difficulties and disadvantages associated with improving the input power factor of a ferroresonant constant current source.
The present invention is directed to a method of designing a high power factor integrated ferroresonant constant current source. The method includes the steps of providing an input coil disposed about a ferromagnetic core and to be coupled to an AC voltage source. An output coil is disposed about the core and to be coupled to a load. A control coil is disposed about the core and coupled to a switch for regulating current output of the constant current source. A first capacitor coil is disposed about the core and inductively coupled to the output coil and coupled to a capacitor to provide a first resonant sub-circuit having maximum gain, and a second capacitor coil disposed about the core and inductively coupled to the control coil and coupled to a capacitor to provide asecond resonant sub-circuit to control resonant gain. A flux density (BPRI) is selected for a portion of the core around the input coils that is substantially lower than the flux density BCAP of a portion of the core around the capacitor coils.
Preferably, the flux density BPRI is about one half the flux density BCAP. Further, BCAP is preferably about 14 kG to about 15 kG. It is also preferable to provide a leakage reactance XS satisfying the mathematical expression             X      S        ≤                            R          2                +                  X          O          2                    RA        ,
where R is the resistance of all of the windings, XO is the reactance of the output inductor magnetically coupled to the resonant capacitor, and A is the capacitor voltage gain, as described hereinbelow with respect to equation (6).